Binomial distribution question

Hello,

I have a question of my solution to a problem that uses the Binomial
distribution. The question is stated as follows, "In a certain physics
course, 7.3% of the students failed and 92.7% passed, avergaged over
many semesters.

[...]

b) what is the probability that five or more students will fail?"

To answer this question I use Binomia distrubtion and I use the
following setup to get the correct answer (the answer in the back of
the book).

Sum[32!/(x!(32 - x)!) * .073^x * (1 - .073)^(32-x),x,5,32]=8%

However, when I go to look at this from the other side (ie what is the
probability if 0 or 27 of the students pass) I get a answer that does
not square with the answer I got above.

Sum[32!/(x!(32 - x)!) * .972^x * (1 - .972)^(32-x),x,0,27]=.18%

To me it seems like I should get 92% and not .18%. 92% would square
with what I got above and makes sense since all I am doing is just
looking at the problem from the other side (ie I am saying that at
least 5 students fail but up to 32 can). I have a feeling I just over
looking something simple, am I right?

Thanks

Carlos

.

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